x2+8x=11

Solution for x2+8x=11 equation:

x2+8x=11

We move all terms to the left:

x2+8x-(11)=0

We add all the numbers together, and all the variables

x^2+8x-11=0

a = 1; b = 8; c = -11;
Δ = b2-4ac
Δ = 82-4·1·(-11)
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{3}}{2*1}=\frac{-8-6\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{3}}{2*1}=\frac{-8+6\sqrt{3}}{2}
$